What is the perpendicular distance (in cm) between the parallel sides of a trapezium whose area is 108 sqcm. and the lengths of the parallel sides are 9 cm and 36 cm?
4.8 cm
Calculating Trapezium Distance
The problem asks for the perpendicular distance (height) between the parallel sides of a trapezium, given its area and the lengths of the parallel sides.
Trapezium Area Formula
The formula for the area ($A$) of a trapezium is:
$A = \frac{1}{2} \times (a + b) \times h$where a and b are the lengths of the parallel sides, and h is the perpendicular distance (height) between them.
Given Information
- Area ($A$) = 108 sq cm
- Length of one parallel side ($a$) = 9 cm
- Length of the other parallel side ($b$) = 36 cm
Solving for Distance (Height)
Substitute the given values into the area formula:
$108 = \frac{1}{2} \times (9 + 36) \times h$First, calculate the sum of the parallel sides:
$9 + 36 = 45 \text{ cm}$Now, substitute this sum back into the equation:
$108 = \frac{1}{2} \times 45 \times h$ $108 = 22.5 \times h$To find the height ($h$), rearrange the equation:
$h = \frac{108}{22.5}$Perform the division:
$h = 4.8 \text{ cm}$Therefore, the perpendicular distance between the parallel sides is 4.8 cm.
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